NONSMOOTH OPTIMIZATION OVER THE (WEAKLY OR PROPERLY) PARETO SET OF A LINEAR-QUADRATIC MULTI-OBJECTIVE CONTROL PROBLEM: EXPLICIT OPTIMALITY CONDITIONS

摘要

We present explicit optimality conditions for a nonsmooth functional defined over the (properly or weakly) Pareto set associated with a multi-objective linear-quadratic control problem. This problem is very difficult even in a finite dimensional setting , i.e. when, instead of a control problem, we deal with a mathematical programming problem. Amongst various applications, our problem may be considered as a response for a decision maker when he has to choose a solution over the solution set of the grand coalition p-player cooperative differential game.